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Papers related to the package | Supplementary materials and vignettes | Density estimation via normal mixtures (and MCMC) | Multivariate GLMM's with a normal mixture in the distribution of random effects | Supporting functions to further process or visualize results from running NMixMCMC or GLMM_MCMC functions | Univariate distributions | Multivariate distributions | Miscellaneous random number generation | Matrix linear algebra | Basic statistics | Utilities | Datasets |

This package contains a mixture of statistical methods including the MCMC methods to analyze normal mixtures.

This overview provides a sorted list of the functions of the package and links to few more involved examples. Methods implemented in the package could be classified into following areas.

• Density estimation via normal mixtures (and MCMC)
• Multivariate generalized linear mixed models with a normal mixture in the distribution of random effects
• Supporting functions to further process or visualize results from running NMixMCMC or GLMM_MCMC functions
• Univariate distributions
• Multivariate distributions
• Miscellaneous random number generation
• Matrix linear algebra
• Basic statistics
• Utilities
• Datasets

Papers related to the package

Please, cite either of the following papers if you find the package useful.

• Komárek, A. (2009). A new R package for Bayesian estimation of multivariate normal mixtures allowing for selection of the number of components and interval-censored data. Computational Statistics and Data Analysis, 53(12), 3932-3947, doi: 10.1016/j.csda.2009.05.006.
  • Paper describing the methods related to density estimation via normal mixtures and MCMC.
  
  
• Komárek, A., Hansen, B. E., Kuiper, E. M. M., van Buuren, H. R., and Lesaffre, E. (2010). Discriminant analysis using a multivariate linear mixed model with a normal mixture in the random effects distribution. Statistics in Medicine, 29(30), 3267-3283, doi: 10.1002/sim.3849.
  
  • Paper describing the methods related to discriminant analysis for multivariate longitudinal or grouped data continuous data based on multivariate linear mixed models with a normal mixture in the distribution of random effects.
  
  
• Komárek, A. and Komárková, L. (2011). Clustering for multivariate continuous and discrete longitudinal data. Submitted for publication.
  • Paper describing the methods related to cluster analysis for multivariate longitudinal or grouped data continuous and discrete data based on multivariate generalized linear mixed models with a normal mixture in the distribution of random effects.
    
  
  

Supplementary materials and vignettes

• Komarek-NMix-supplement.pdf
  Supplement to Komárek (2009) which includes some technical details not included in the main paper.
   
• Galaxy.pdf,  Galaxy.R 
  R example of 1-dimensional density estimation using the RJ-MCMC described in Section 6.1 of Komárek (2009).
   
• Faithful.pdf,  Faithful.R 
  R example of 2-dimensional density estimation described in Section 6.2 of Komárek (2009).
   
• Tandmob.pdf,  Tandmob.R 
  R example of 6-dimensional density estimation with interval-censored data described in Section 6.3 of Komárek (2009).
   
• PBCseq.pdf,  PBCseq.R 
  R example of cluster analysis based on multivariate longitudinal data from a Mayo Clinic trial on 312 patients with primary biliary cirrhosis described in Section 3.1 of Komárek and Komárková (2011).
   

1. Density estimation via normal mixtures (and MCMC)

NMixMCMC	MCMC estimation of (multivariate) normal mixtures with possibly censored data
	There exists a print method for objects of class NMixMCMC.
NMixEM	EM algorithm for a homoscedastic normal mixture
	There exists a print method for objects of class NMixEM.
NMixChainsDerived	Create MCMC chains derived from previously sampled values
NMixPredDA	Discriminant analysis based on MCMC output from the mixture model
NMixPlugDA	Discriminant analysis based on plug-in estimates from the mixture model

2. Multivariate generalized linear mixed models with a normal mixture in the distribution of random effects

GLMM_MCMC	MCMC estimation of a (multivariate) generalized linear mixed model with a normal mixture in the distribution of random effects
	There exists a print and fitted method for objects of class GLMM_MCMC.
GLMM_longitDA	Discriminant analysis for longitudinal profiles based on fitted GLMM's

3. Supporting functions to further process or visualize results from running NMixMCMC or GLMM_MCMC functions

The following functions are generic with default method and a method for objects of class NMixMCMC and GLMM_MCMC implemented.

NMixRelabel	Re-labeling the MCMC output of the mixture model
NMixSummComp	Summary for the mixture components
tracePlots	Traceplots for selected parameters
NMixPredDensJoint2	Pairwise bivariate predictive density
	There is also a plot method for objects of class NMixPredDensJoint2.
NMixPlugDensJoint2	Pairwise bivariate densities: plug-in estimate
	There is also a plot method for objects of class NMixPlugDensJoint2.
NMixPredCondDensJoint2	Pairwise bivariate conditional predictive densities
	There is also a plot method for objects of class NMixPredCondDensJoint2.
NMixPlugCondDensJoint2	Pairwise bivariate conditional densities: plug-in estimate
	There is also a plot method for objects of class NMixPlugCondDensJoint2.
NMixPredDensMarg	Marginal (univariate) predictive density
	There is also a plot method for objects of class NMixPredDensMarg.
NMixPlugDensMarg	Marginal (univariate) densities: plug-in estimate
	There is also a plot method for objects of class NMixPlugDensMarg.
NMixPredCDFMarg	Marginal (univariate) predictive cumulative distribution function
	There is also a plot method for objects of class NMixPredCDFMarg.
NMixPredCondDensMarg	Univariate conditional predictive density
	There is also a plot method for objects of class NMixPredCondDensMarg.
NMixPlugCondDensMarg	Univariate conditional densities: plug-in estimate
	There is also a plot method for objects of class NMixPlugCondDensMarg.

Additionally, the following functions are available.

Y2T	Transform fitted distribution of Y=trans(T) into distribution of T
	This is a generic function with default method to transform a fitted distribution of Y = trans(T) into a distribution of T = itrans(Y).
	There are methods for objects of class NMixPredDensMarg, NMixPlugDensMarg, NMixPredCDFMarg, NMixPredDensJoint2, NMixPlugDensJoint2, NMixPredCondDensMarg, NMixPlugCondDensMarg, NMixPredCondDensJoint2, NMixPlugCondDensJoint2.
summaryDiff	Posterior summary statistics for a difference of two quantities

4. Univariate distributions

rTNorm	Random number generation from a truncated normal distribution

5. Multivariate distributions

dMVN, rMVN, rcMVN	(Log-)density and random number genaration for a multivariate normal distribution
rTMVN	Random number genaration from a truncated multivariate normal distribution
dMVNmixture, dMVNmixture2, rMVNmixture, rMVNmixture2	(Log-)density and random number genaration for a mixture of (multivariate) normal distributions
dWishart, rWishart	(Log-)density and random number genaration for a Wishart distribution
rDirichlet	Random number genaration from a Dirichlet distribution

6. Miscellaneous random number generation

rRotationMatrix	Random rotation matrix
rSamplePair	Sample a pair (with replacement)

7. Matrix linear algebra

MatMPpinv	Moore-Penrose pseudoinverse of a squared matrix
MatSqrt	Square root of a matrix

8. Basic statistics

BLA	Best linear approximation with respect to the mean square error (theoretical linear regression)

9. Utilities

getProfiles	Individual longitudinal profiles of a given variable
plotProfiles	Plot individual longitudinal profiles
BsBasis	B-spline basis
generatePermutations	Generate all permutations of (1, ..., K)
SP2Rect	Conversion of a symmetric matrix stored in a packed format (lower triangle only) into a matrix
autolayout	Automatic layout for several plots in one figure
cbplot	Plot a function together with its confidence/credible bands

10. Datasets

Acidity	Acidity index of lakes in North-Central Wisconsin
	Acidity index measured in a sample of 155 lakes in North-Central Wisconsin.
Enzyme	Enzymatic activity in the blood
	Enzymatic activity in the blood, for an enzyme involved in the metabolism of carcinogenic substances, among a group of 245 unrelated individuals.
Faithful	Old Faithful Geyser Data
	Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA, version used in Härdle (1991).
Galaxy	Velocities of distant galaxies
	Velocities of 82 distant galaxies, diverging from our own galaxy.
PBCseq	Mayo Clinic Primary Biliary Cirrhosis, sequential data
Tandmob	Signal Tandmobiel data
	Dental (Signal Tandmobiel) data for 4430 6-12 year old children
TandmobEmer	Signal Tandmobiel data - emergence times
	Data derived from Tandmob.